Transfer Learning by Mapping and Revising Relational Knowledge

1. Transfer Learning by Mapping and Revising Relational Knowledge Raymond J. Mooney University of Texas at Austin with acknowledgements to Lily Mihalkova, Tuyen Huynh

2. Transfer Learning • Most machine learning methods learn each new task from scratch, failing to utilize previously learned knowledge. • Transfer learning concerns using knowledge acquired in a previous source task to facilitate learning in a related target task. • Usually assume significant training data was available in the source domain but limited training data is available in the target domain. • By exploiting knowledge from the source, learning in the target can be: • More accurate: Learned knowledge makes better predictions. • Faster: Training time is reduced.

3. Transfer Learning Curves TRANSFER FROM SOURCE NO TRANSFER Predictive Accuracy Advantage from Limited target data Jump start Amount of training data in target domain Transfer learning increases accuracy in the target domain.

4. Recent Work on Transfer Learning • Recent DARPA program on Transfer Learning has led to significant recent research in the area. • Some work focuses on feature-vector classification. • Hierarchical Bayes (Yu et al., 2005; Lawrence & Platt, 2004) • Informative Bayesian Priors (Raina et al., 2005) • Boosting for transfer learning (Dai et al., 2007) • Structural Correspondence Learning (Blitzer et al., 2007) • Some work focuses on Reinforcement Learning • Value-function transfer (Taylor & Stone, 2005; 2007) • Advice-based policy transfer (Torrey et al., 2005; 2007)

5. Similar Research Problems • Multi-Task Learning (Caruana, 1997) • Learn multiple tasks simultaneously; each one helped by the others. • Life-Long Learning (Thrun, 1996) • Transfer learning from a number of prior source problems, picking the correct source problems to use.

6. Logical Paradigm • Represents knowledge and data in binary symbolic logic such as First Order Predicate Calculus. + Rich representation that handles arbitrary sets of objects, with properties, relations, quantifiers, etc.  Unable to handle uncertain knowledge and probabilistic reasoning.

7. Probabilistic Paradigm • Represents knowledge and data as a fixed set of random variables with a joint probability distribution. + Handles uncertain knowledge and probabilistic reasoning.  Unable tohandle arbitrary sets of objects, with properties, relations, quantifiers, etc.

8. Statistical Relational Learning (SRL) • Most machine learning methods assume i.i.d. examples represented as fixed-length feature vectors. • Many domains require learning and making inferences about unbounded sets of entities that are richly relationally connected. • SRL methods attempt to integrate methods from predicate logic and probabilistic graphical models to handle such structured, multi-relational data.

9. Statistical Relational Learning Actor Director WorkedFor Movie Multi-Relational Data Learning Algorithm Probabilistic Graphical Model

10. Multi-Relational Data Challenges • Examples cannot be effectively represented as feature vectors. • Predictions for connected facts are not independent. (e.g. WorkedFor(brando, coppolo), Movie(godFather, brando)) • Data is not i.i.d. • Requires collective inference (classification)(Taskar et al., 2001) • A single independent example (mega-example) often contains information about a large number of interconnected entities and can vary in length. • Leave one university out testing (Craven et al., 1998)

11. TL and SRL and I.I.D. Standard Machine Learning assumes examples are: Independent and Identically Distributed TL breaks the assumption that test examples are drawn from the same distribution as the training instances SRL breaks the assumption that examples are independent

12. Multi-Relational Domains • Domains about people • Academic departments (UW-CSE) • Movies (IMDB) • Biochemical domains • Mutagenesis • Alzheimer drug design • Linked text domains • WebKB • Cora

13. Markov logic networks Relational Learning Methods • Inductive Logic Programming (ILP) • Produces sets of first-order rules • Not appropriate for probabilistic reasoning • If a student wrote a paper with a professor, then the professor is the student’s advisor • SRL models & learning algorithms • SLPs (Muggleton, 1996) • PRMs (Koller, 1999) • BLPs (Kersting & De Raedt, 2001) • RMNs (Taskar et al., 2002) • MLNs (Richardson & Domingos, 2006)

14. Source: Target: UW-CSE Professor(A) Student(A) Publication(T, A) AdvisedBy(A, B) … IMDB Director(A) Actor(A) Movie(T, A) WorkedFor(A, B) … MLN Transfer(Mihalkova, Huynh, & Mooney, 2007) • Given two multi-relational domains, such as: • Transfer a Markov logic network learned in the Source to the Target by: • Mapping the Source predicates to the Target • Revising the mapped knowledge

15. movieTitle person First-Order Logic Basics • Literal: A predicate (or its negation) applied to constants and/or variables. • Gliteral: Ground literal; WorkedFor(brando, coppola) • Vliteral: Variablized literal; WorkedFor(A, B) • We assume predicates have typed arguments. • For example: Movie(godFather, coppola)

16. First-Order Clauses • Clause: A disjunction of literals • Can be rewritten as a set of rules:

17. Representing the Data • Makes a closed world assumption: • The gliterals listed are true; the rest are false

18. 5.3 3.2 0.5 Markov Logic Networks(Richardson & Domingos, 2006) • Set of first-order clauses, each assigned a weight. • Larger weight indicates stronger belief that the clause should hold. • The clauses are called thestructureof the MLN.

19. Algorithm Experiments Markov Networks(Pearl, 1988) • A concise representation of the joint probability distribution of a set of random variables using an undirected graph. Joint distribution Reputation of Author Quality of Paper Same probability distribution can be represented as the product of a set of functions defined over the cliques of the graph

20. weights features Markov Network Equations • General form • Log-linear models

21. Ground Markov Network for an MLN • MLNs are templates for constructing Markov networks for a given set of constants: • Include a node for each type-consistent grounding (a gliteral) of each predicate in the MLN. • Two nodes are connected by an edge if their corresponding gliterals appear together in any grounding of any clause in the MLN. • Include a feature for each grounding of each clause in the MLN with weight equal to the weight of the clause.

22. 1.3 1.2 0.5 Actor(brando) constants: coppola, brando, godFather Director(brando) WorkedFor(brando, brando) WorkedFor(brando, coppola) Movie(godFather, brando) Movie(godFather,coppola) WorkedFor(coppola, brando) WorkedFor(coppola, coppola) Director(coppola) Actor(coppola)

23. all groundings of fi all clauses in the model Compare to log-linear Markov networks: MLN Equations

24. MLN Equation Intuition A possible world (a truth assignment to all gliterals) becomes exponentially less likely as the total weight of all the grounded clauses it violates increases.

25. MLN Inference • Given truth assignments for given set of evidence gliterals, infer the probability that each member of set of unknown query gliterals is true.

26. 0.9 F 0.1 0.7 T T 0.2 0.3 T 0.2 Actor(brando) Director(brando) WorkedFor(brando, brando) WorkedFor(brando, coppola) Movie(godFather, brando) Movie(godFather,coppola) WorkedFor(coppola, brando) WorkedFor(coppola, coppola) Director(coppola) Actor(coppola)

27. MLN Inference Algorithms • Gibbs Sampling (Richardson & Domingos, 2006) • MC-SAT (Poon & Domingos, 2006)

28. MLN Learning • Weight-learning (Richardson & Domingos, 2006; Lowd & Domingos, 2007) • Performed using optimization methods. • Structure-learning (Kok & Domingos, 2005) • Proceeds in iterations of beam search, adding the best-performing clause after each iteration to the MLN. • Clauses are evaluated using WPLL score.

29. Compute the likelihood of the data according to the model and take log For each gliteral, condition on its Markov blanket for tractability Weight it so that predicates with greater arity do not dominate WPLL(Kok & Domingos, 2005) • Weighted pseudo log-likelihood

30. Alchemy • Open-source package of MLN software provided by UW that includes: • Inference algorithms • Weight learning algorithms • Structure learning algorithm • Sample data sets • All our software uses and extends Alchemy.

31. Publication(T,A)  AdvisedBy(A,B) → Publication(T,B) (clause from UW-CSE) Predicate Mapping: Publication  Movie AdvisedBy  WorkedFor M-TAMAR • Movie(T,A)  WorkedFor(A,B) → Movie(T,B) R-TAMAR • Movie(T,A)  WorkedFor(A,B)  Relative(A,B)→ Movie(T,B) TAMAR(Transfer via Automatic Mapping And Revision) Target (IMDB) Data

32. Predicate Mapping • Each clause is mapped independently of the others. • The algorithm considers all possible ways to map a clause such that: • Each predicate in the source clause is mapped to some target predicate. • Each argument type in the source is mapped to exactly one argument type in the target. • Each mapped clause is evaluated by measuring its WPLL for the target data, and the most accurate mapping is kept.

33. Publication(title, person) Movie(name, person) AdvisedBy(person, person) WorkedFor(person, person) Predicate Mapping Example Consistent Type Mapping: title → name person → person

34. Publication(title, person) Gender(person, gend) AdvisedBy(person, person) SameGender(gend, gend) Predicate Mapping Example 2 Consistent Type Mapping: title → person person → gend

35. Publication(T,A)  AdvisedBy(A,B) → Publication(T,B) (clause from UW-CSE) M-TAMAR • Movie(T,A)  WorkedFor(A,B) → Movie(T,B) R-TAMAR • Movie(T,A)  WorkedFor(A,B)  Relative(A,B)→ Movie(T,B) TAMAR(Transfer via Automatic Mapping And Revision) Target (IMDB) Data

36. Bottom-up Top-down Source MLN Source MLN Data-Driven Revision Proposer Target Training Data Transfer Learning as Revision • Regard mapped source MLN as an approximate model for the target task that needs to be accurately and efficiently revised. • Thus our general approach is similar to that taken by theory revision systems (Richards & Mooney, 1995). • Revisions are proposed in a bottom-up fashion.

37. Clause 1 Clause 1 New Clause 1 wt wt wt Too Long Self-diagnosis Clause 2 New Clause 3 Clause 2 wt wt wt Good Clause 3 New Clause 5 Clause 3 wt wt wt Too Short Clause 4 Clause 4 wt wt Good New Clause 6 Clause 5 New Clause 7 Clause 5 wt wt wt wt Too Long Directed Beam Search R-TAMAR Relational Data New clause discovery New Candidate Clauses Changein WPLL 0.1 -0.2 0.5 1.7 1.3

38. R-TAMAR: Self-Diagnosis • Use mapped source MLN to make inferences in the target and observe the behavior of each clause: • Consider each predicate P in the domain in turn. • Use Gibbs sampling to infer truth values for the gliterals of P, using the remaining gliterals as evidence. • Bin the clauses containing gliterals of P based on whether they behave as desired. • Revisions are focused only on clauses in the “Bad” bins.

39. Self-Diagnosis: Clause Bins Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Movie(rainMaker, coppola) WorkedFor(brando, coppola) Current gliteral: Actor(brando) • Relevant; Good

40. Self-Diagnosis: Clause Bins Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Movie(rainMaker, coppola) WorkedFor(brando, coppola) Current gliteral: Actor(brando) • Relevant; Good • Relevant; Bad

41. Self-Diagnosis: Clause Bins Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Movie(rainMaker, coppola) WorkedFor(brando, coppola) Current gliteral: Actor(brando) • Relevant; Good • Relevant; Bad • Irrelevant; Good

42. Lengthen Shorten Self-Diagnosis: Clause Bins Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Movie(rainMaker, coppola) WorkedFor(brando, coppola) Current gliteral: Actor(brando) • Relevant; Good • Relevant; Bad • Irrelevant; Good • Irrelevant; Bad

43. Structure Revisions • Using directed beam search: • Literal deletions attempted only from clauses marked for shortening. • Literal additions attempted only for clauses marked for lengthening. • Training is much faster since search space is constrained by: • Limiting the clauses considered for updates. • Restricting the type of updates allowed.

44. New Clause Discovery • Uses Relational Pathfinding (Richards & Mooney, 1992) Actor(brando) Director(coppola) Movie(godFather, brando) Movie(godFather, coppola) Movie(rainMaker, coppola) WorkedFor(brando, coppola) WorkedFor WorkedFor brando coppola Movie Movie Movie godFather rainMaker

45. M-TAMAR R-TAMAR Weight Revision • Publication(T,A)  AdvisedBy(A,B) → Publication(T,B) Target (IMDB) Data • Movie(T,A)  WorkedFor(A,B) → Movie(T,B) • Movie(T,A)  WorkedFor(A,B)  Relative(A,B)→ Movie(T,B) MLN Weight Training • 0.8 Movie(T,A)  WorkedFor(A,B)  Relative(A,B)→ Movie(T,B)

46. Experiments: Domains • UW-CSE • Data about members of the UW CSE department • Predicates include Professor, Student, AdvisedBy, TaughtBy, Publication, etc. • IMDB • Data about 20 movies • Predicates include Actor, Director, Movie, WorkedFor, Genre, etc. • WebKB • Entity relations from the original WebKB domain (Craven et al. 1998) • Predicates include Faculty, Student, Project, CourseTA, etc.

47. Dataset Statistics Data is organized as mega-examples • Each mega-example contains information about a group of related entities. • Mega-examples are independent and disconnected from each other.

48. Manually Developed Source KB • UW-KB is a hand-built knowledge base (set of clauses) for the UW-CSE domain. • When used as a source domain, transfer learning is a form of theory refinement that also includes mapping to a new domain with a different representation.

49. Systems Compared • TAMAR: Complete transfer system. • ScrKD: Algorithm of Kok & Domingos (2005) learning from scratch. • TrKD: Algorithm of Kok & Domingos (2005) performing transfer, using M-TAMAR to produce a mapping.

50. Methodology: Training & Testing • Generated learning curves using leave-one-out CV • Each run keeps one mega-example for testing and trains on the remaining ones, provided one by one. • Curves are averages over all runs. • Evaluated learned MLN by performing inference for all gliterals of each predicate in turn, providing the rest as evidence, and averaging the results.